1. Field of the Invention
The present invention relates generally to methods and systems for image synthesis in and by digital computing systems, such as for motion pictures and other applications, and in particular, relates to methods, systems, devices, computer software, and display technology for image synthesis by rank-1 lattices.
2. Description of Prior Art
The use of synthetic images has become increasingly important and widespread in motion pictures and other commercial and scientific applications. A synthetic image typically represents a two-dimensional array of digital values, called picture elements or pixels, and thus is commonly regarded as a two-dimensional function.
Image synthesis is the process of creating synthetic images from scenes. As a general matter, digital images are generated by rasterization or, in the case of photorealistic images of three-dimensional scenes, by ray tracing. Both approaches aim at determining the appropriate color for each pixel by projecting the original function into the pixel basis. Due to the discrete representation of the original function, the problem of aliasing arises, as described below.
In particular, computing the intensity of a single pixel requires an integration function over the pixel area. This integral is often highly complex and cannot be solved analytically, thus requiring numerical methods for solution, which may include Monte Carlo and quasi-Monte Carlo methods. However, typical numerical methods used in such applications have their own limitations and attendant problems.
Another computational approach used in computer graphics is lattice theory. For example, the accumulation buffer typically used in computer graphics exploits the structure of regular grids. In addition, efficient rasterization techniques have been designed by taking advantage of such grids. Certain known sampling techniques employ Fibonacci lattices, which are a type of rank-1 lattice.
It would be desirable to provide methods, systems, devices, and computer software using rank-1 lattices that can be generated rapidly and efficiently, and that are readily adapted to the requirements of image synthesis and other computer graphics applications.
It would also be desirable to provide such methods, systems, devices and software that enable the efficient application of rank-1 lattices to anti-aliasing, rasterization, and other computer graphics functions.